Schools labelled as failing and threatened with closure by the government last year have been told they will receive as little as £5,000 to help them improve, figures seen by the Guardian reveal. Some headteachers have not yet seen a penny of the cash promised last June as part of a £400m plan to eradicate underperforming schools.

The 631 schools identified as underachieving were told by the schools secretary, Ed Balls, that they would receive intensive new support and a share of the money, but that they faced closure or being turned into an academy if they did not attain 30% of pupils getting five good GCSEs including English and maths.

Figures obtained by the Liberal Democrats through a parliamentary question today reveal that under the programme one school, Robert Napier in Medway, received just £5,000. Another 21 got £8,000 and 75 less than £25,000 - about enough for one extra classroom teacher. The average cash injection was £87,000, the highest being £352,000 for the King Harold School in Essex.

The Department for Children, Schools and Families (DCSF) insisted that schools were allocated cash according to their needs but headteachers said it paled in comparison with the damage triggered by the National Challenge campaign.

John Dunford, general secretary of the Association of School and College Leaders, said: "The rationale behind the National Challenge was that substantial amounts of money would go into schools to help them raise achievement. The damage done by the launch to the reputation of many of these schools means that they lost some 11-year-olds who had been due to come last September. The money will barely compensate for pupils they lost."

Jonathan Morris, headteacher of Moorside Community Technology School in Durham, which will receive £8,000, said: "We've been improving for a number of years but we were clobbered by the way in which the DCSF orchestrated the press. Unnecessary damage was done to our reputation. No amount of money would compensate for that.

One school said that it had not yet received the £15,000 it had been promised. Liam Nolan, headteacher of Perry Beeches in Birmingham, the fastest improving school in the past year, said: "I've not received a penny even though National Challenge was announced a year ago. We've been named and expected to change things with no support. That's not acceptable. We live with the title of National Challenge without the support mechanisms to change that position."

Robert Napier School, which received the smallest amount, said in a statement that the low allocation indicated the "minimal level of support thought necessary by Medway local authority" because the school had been improving already.

David Laws, the Liberal Democrat education spokesman, said: "For many schools, National Challenge has been all pain and no gain. Their designation as one of the 'failing schools' has undermined plans to recruit new teachers, and to attract more parents and pupils."

A DCSF spokesperson said: "A high proportion [of named schools] are already making good progress and do not require as much funding and support as others in more challenging circumstances.

"But the support goes much further than simply giving additional funding. In each case we have built a 'team around the school' to get behind schools' efforts. Schools that we and the local authority have identified with the greatest needs are receiving more intensive support."